Today, the last business day of August, you received your first salary of $ 1000. You have been promised a 3% increase per month for the next 20 years. You have decided to save 30% of your salary every month by depositing $ 100 in a term deposit at 2% per month in Bank X, and the rest in Bank Y at 2.5% per month. On the other hand, you will continue to receive $ 80 per month, at the end of each month, for a research aid that you intend to keep forever. You deposit this check in full at Bank Y.
It asks:
a) Set up the dynamic system in discrete time that allows you to see the evolution of your salary, the balance in Bank X and the balance in Bank Y over time. Explain any additional assumptions you make (7 marks)
b) Solve the system (you can use the computer to do it, any program)